# Hydraulic Conductivity and Transmissivity

## Table of Contents

## Hydraulic Conductivity

The ability of soil to transfer water under a hydraulic gradient is measured by its hydraulic conductivity. It is defined by Darcy’s law, which, for one-dimensional vertical flow, can be written as follows:

U = -K\frac{dl}{dz} –(1)

U = Darcy’s velocity

h= hydraulic head

Z = Vertical dist. in the soil

K = hydraulic conductivity

On the basis of eq 1, the hydraulic conductivity is defined as the ratio of Darcy’s velocity to the applied hydraulic gradient. The dimension of K is the same as that for velocity which is length per unit time.

It is one of the hydraulic properties of the soil, the other involves the soil’s fluid retention characteristics. Under particular circumstances, these characteristics control how the soil fluid behaves inside the soil system. More specifically, hydraulic conductivity determines the ability of the soil fluid to flow through the soil matrix system under a specified hydraulic gradient.

The soil system’s capacity to hold onto soil fluid at a certain pressure condition is determined by the soil fluid retention characteristics.

It depends on the soil grain size, the structure of the soil matrix, the type of soil fluid, and the relative amount of soil fluid present in the soil matrix. The imp. properties relevant to the solid matrix of the soil include pore size distribution, pore shape tortuosity, and specific surface am porosity. The density and viscosity of the soil fluid are two crucial characteristics to consider. For a substance system saturated with the soil fluid, the hydraulic conductivity K can be expressed as follows.

K = \frac{K\rho g}{\mu} — (2)

K = intrinsic permeability of soil

g = fluidity of the liquid

K = hydraulic conductivity

By equation (2) Darcy’s law can be rewritten explicitly in terms of its coefficient of proportionality (K)

K = \frac{K\rho g}{\mu} = \frac{|U|}{|dh|dz|}

Saturated hydraulic conductivity levels in soils can differ by several orders of magnitude, contingent upon the kind of soil. Saturated hydraulic conductivity values exhibit spatial diversity across the space domain, which is typically present in the geological formation of soils. When the fluid properties of density and viscosity are known, eq. (3) can be listed, to experimentally determine the value of the intrinsic permeability k’ and the hydraulic conductivity ‘K.

## Hydraulic Transmissivity

An aquifer may consist of \eta soil layer. The transmissivity for horizontal flow (T) of the ith soil layer with a saturated thickness di and horizontal hydraulic conductivity Khi is

**Ti = Khidi**

Transmissivity is directly proportional to horizontal hydraulic conductivity (Khi) and thickness (di). Expressing Khi in m/day di in m, the transmissivity T_i is found in unite m? day.

The amount of water that may be transferred horizontally, like to a pumping well, is measured by the transmissivity.

The total transmissivity T_i of the aquifer is

T_t = \Sigma T_i \: \Sigma Khidi

Where \Sigma signifies the summation over all layers: i = 1, 2, 3… \eta

The aquifer’s apparent horizontal hydraulic conductivity (Kha) is

D, = total thickness of the aquifer (Dt = \Sigma di, with i = 1, 2, 3… \eta )

Pumping tests are one method used to measure an aquifer’s transmissivity.

A soil layer is not saturated and does not increase transmissivity when it is located above the water table. The saturated thickness of the soil layer is equal to the thickness of the soil layer when it is completely below the water table. The saturated thickness of a soil layer that contains a water table is equal to the distance between the water table and the layer’s bottom. The transmissivity may fluctuate in accordance with the thickness’s locational or temporal variations due to the water table’s potential for dynamic behavior.

In an aquifer that is semi-confined, the water table is situated inside a layer of soil that has an extremely low transmissivity. As a result, variations in the total transmissivity (DI) that arise from variations in the water table’s level are extremely minute.

The water table may be brought down when pumping water from an unconfined aquifer, where the water table is inside a soil layer with a high transmissivity. This will decrease the transmissivity and the amount of water flowing to the well.

### Hydraulic Conductivity and Transmissivity

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